Thursday, February 15, 2018

The geometry of a 1870's barn

This Vermont barn was built in the 1870's . It has been used for storage for the last 20 years.

I prepared a report on its history and structure for its owners so they could consider repair and reconstruction with some real knowledge - not just good memories and/or worry about costs.

The barn was well built by a farmer who knew his land and a framer skilled at his trade.
The frame is regular, much of it still sturdy. Its mortises,  tenons, and pegs are still secure.

Its bents use dropped girts and posts to purlins which support  common rafters, a framing system regularly used in the Hudson Valley watershed, not often seen in this area of Vermont.

While I was not asked about the barn's geometry, as I laid out the plan and the frame I could see the geometry clearly - not complex, quite simple, repetitive, and straightforward.

Here is the 3rd bent and the lower level floor plan.
The bent is one of the 4 timber frames across the barn that are then fastened together with plates and girts. Walls and flooring have been left out.
The plan is mainly the post locations. I have not included the exterior wall girts.  The braces which are visible in the photograph to the right are barely noted.

The floor plan could easily have been laid out using circle geometry.

I have added Laurie Smith's diagram for drawing a square beginning with a circle. It is a very clear description.

For his websites see: http://www.thegeometricaldesignworks.com/

and  http://historicbuildinggeometry.uk/

Here is my drawing of the floor plan with its posts laid out using circles. The first  (top) 2 bays are of equal depth and width.  The dashed green line shows the layout determined by the circles.

The lower bay (between bent 3 and 4) is not as deep. Perhaps the land dropped off too steeply, or the lumber available was not as long. The dotted red line in the lower right rectangle shows how the crossing of the arcs of the square determined the depth of the bay.

The base of bent 3 is vague on purpose. I don't really know the depth of many of the lower level posts. The land slopes west to east. The floor on the east end has been built up over the years with layers of discarded boards.  The right end has been reconfigured for cows; the left end has a false ceiling.
The main  barn level of the bents is divided into thirds. The  posts are the height of a third of the bay's width - the space they outline is a square. I've drawn it in red. The dropped girts are set at the point where the arcs of the square cross. Also drawn in red.
This is similar to how the lower level east bay's depth was determined.
The posts that support the purlins ( the roof beams ) are centered on the squares below. The height of the ridge is also determined by where the arcs of the loft square cross.

Lastly the location of the lower girt which becomes the plate for the wing is determined by the Rule of Thirds.

Such basic practical geometry tools! They are  those described by Serlio, Palladio, and Asher Benjamin - circles, arcs, lines - applied in very simple ways with impressive results.

Well thought out, straightforward without fancy flourish, the space and the frame speak to me. But I am simply the one who documented this, sharing the power, the grace, that I found.

The barn, after 150 years, is no longer essential. It is very possible that it may not survive until a new purpose discovers it.

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Wednesday, February 7, 2018

How Practical Geometry is practical

This is a sequel to my previous post: http://www.jgrarchitect.com/2017/11/the-tuckahoe-cabin-geometry.html

Do I think the carpenter who laid out the small simple cabin at Tuckahoe actually drew the arcs on the  ground? or on the floor  - once he had squared the foundation and set the sills?

No, I think he knew the geometry. Someone had already taught him what I drew.
I think he swung the arcs but marked only the foot or so where he  knew the crossings would be. He knew that he wanted to locate the center of each wall, and  - by basic geometric rules - he needed 2 points to draw a line perpendicular or parallel to the wall in question.

Here is a lithograph of le Pere Soubise, patron saint of the Campagnons, French carpenters who have finished their apprenticeships and begin traveling from town to town, from job to job to learn new skills. (In English an Apprentice becomes a Journeyman at this stage of his training because he 'journeys'. When he has gained enough experience he is then eligible to become a Master.)

le Pere Soubin is probably mythical. But the date of his portrait is known: 1882. Click on the print to read the attribution.
In 1882 a portrait of an important man included the tool of his trade: le Pere Soubise holds a compass.

I have enlarged that part of the image. He holds his hand in  a way that he would if he were using the compass to measure a distance based on the drawing held in his other arm. Or as he would to  mark joist pocket locations on a beam, stepping off from one to the next.

Today a carpenter marks stud spacing with a tape measure that has multiples of 16" highlighted in red. The carpenter doesn't count 16" each time, he uses the tape's marking as a shorthand.
Similarly the framer in 1860 did not need to swing the arc from one point to the next, he used the compass to keep his spacing consistent.

As I was writing this a timber framer who did a lot of repair of old barns mentioned that he often found common rafters laid out at 39.5".
I laughed and told him he had given me a challenge: Why 39.5"?

Here's the arithmetic: Many of the barns were about 40 ft long. 40 ft = 480" . 12 x 39.5 " =  474", 6" shorter than the barn's length. 3" each end for the end rafters.
However, that begins with the solution. It doesn't address how the framer found his answer.

Here's the  geometry.
The framer knows he will use  3" wide rafters on each end of his 40 ft long  barn, so he will have 474" in between for his rafters.
He wants to figure out what distance will work so he can tell the men working with him where to set the rafters and cut the pockets in the plate. The plate is sitting right there in his framing yard -  which might be the floor of the barn he is building.

He could make a scale drawing on a board and scale up to the plate using his compass, like this:

Or he could stretch his line the length of the plate between his end rafters. Then fold the line in half and and then half again. Now he had the length of the plate divided into 4 equal Parts. ( #1 , # 2)
He thinks 12 rafters should do it. That means 3 rafters for each Part. But what's the spacing? On the framing floor he draws out a square using the Part as the side.  The handy Rule of Thirds quickly divides the square into 3 equal rectangles and the Part into 3 equal lengths. (#3)
4 parts x 3 divisions = 12 rafters. Good to go.
He doesn't care that the length of each is 39.5". He cares that he has divided his plate evenly. (#4)

Note that the framer does not add, subtract, multiply or divide. He could show this system to someone who spoke a different language. Neither would need know how to read words or compute. They would need to be able to think logically and reason visually.  Geometry is a language in itself.

By the 1860's  - the time of the Pere Soubise portrait - both France and England had standardized dimensions (meters in France, feet and yards in England). Tape measures existed  but were not widely used. Wooden folding rules were popular after the Civil War,  but carpenters still understood and used compasses for layout and design.

I have met young timber framers who journey as Compagnons.
For more information about the French Compagonnage historically and today:
http://www.historicalcarpentry.com/compagnonnage.html
And note the compass leaning against a beam in the first engraving.